Anti-control of Double Hopf Bifurcation of Vibration Rating Griddle System

Abstract

The vibrating griddle system is a kind of nonlinear multi-parameter dynamical system with high non-smoothness, and traditional bifurcation criterion can’t be applied directly. Therefore, a new explicit bifurcation criterion independent on eigenvalue calculation was adopted to achieve the anti-control of double Hopf bifurcation for vibrating griddle system. Firstly, the Poincaré mapping at the fixed point was obtained according to the motion equation of the system. Then, a linear feedback controller was applied to the system to obtain the controlled Poincaré mapping, and the explicit critical condition of double Hopf bifurcation was obtained according to the bifurcation critical criterion. Finally, numerical simulation of the two types of systems was carried out by the modal superposition method. The results show that the linear feedback controller can effectively achieve the anti-control of double Hopf bifurcation by adjusting the control parameters under the same system parameters. Double Hopf bifurcation can improve the working efficiency of some vibration machinery, so it has certain practical significance.

Keywords: double Hopf bifurcation anti-control,  non-smooth,  explicit critical criterion of bifurcation,  linear feedback controller